Processing parts having complex shapes can be challenging. For example, applying uniform pressure to consolidate and shape processed parts with non-planar portions may require forces applied in different directions. Specially-shaped mandrels may be used for tight corners and other hard-to-reach places on these surfaces. However, mandrels and processed parts often have very different coefficient of thermal expansions (CTEs). The CTE mismatch complicates processing during heating-cooling cycles. Furthermore, uniform heating of parts with complex shapes can be difficult.